Calculate Moment of Inertia of Baseball Bats

I have seen many young guys buying baseball bats from their local baseball bat stores without even checking the quality and performance of the bats.

Even if some of them are doing a few selective and ordinary tests (most of which, I feel, reveal nothing about the performing ability of the bats). They hardly have any idea of how to look into the quality and performing ability of a baseball bat.

So what is it that decides the good or not so good baseball bats? Moment of Inertia! Yes, this is the one thing that will decide how good the bat will perform or how flexible it would be for the batters.

You can calculate the figure using the moment calculator but that for you need some variable measurements. That we will certainly discuss later but prior to that let’s try and have a brief concept of what is MoI and why it is important.

I have noticed that bats of similar weight and length do not swing the same! Even when swinging the bats, some are felt heavier than the others. Why is that? Moreover, I’ve also noticed that bats with thicker handle are easier to swing than that of with same weight but the thinner handle. These all are related to the Moment of Inertia of the bat.

What is Moment of Inertia?


Simply put, it is the measurement of the difficulty level which describes how much force is required to change the velocity of an object by applying force from the outside.

It is generally described in terms of mass. The greater the inertia of the object the more difficult it is to change the velocity of that object. Mass doesn’t depict the weight of the object although, the two are often confused with each other. This is actually the speed at which the baseball player can swing the bat.

Now that we have got a preliminary idea of what is MoI, the next concern should be to how to measure that. This shouldn’t be a difficult task if you have a few metrics. Here I’m going to describe some effective methods and that for you need just a stopwatch, a measuring tape and a digital scale. That’s it!

There are so many mathematical explanations that you would find on the internet and of course, in your Physics book. More so, there are examples where the measurement is calculated using some complicated equipment and technology. But, we are not after that right? I’m trying to explain things simply so that it is understandable by all of us.

It’s a four-step guide to measure the swinging weight of your bat.


Calculate the bat’s pendulum period

You will find that this is the most difficult one. This describes the duration that the bat takes to oscillate from one extreme point to back on that same extreme point. It is generally the full swing time that the bat takes for the “bob”. Here is a step by step guide on how to perform the task.

Hold the bat at a position where it can swing like a pendulum with the knob of the bat resting smoothly on the top of your thumb. In order to provide more stabilization to the movements, you can rest your ring and little finger on a desk in front of you and place your elbow on your knee. The perfect position will allow the bat to swing from one side to another repeatedly.

Now push your baseball bat to one side and let the swing begin. Make sure that the bat doesn’t bounce into your palm or into anything else. Unexpected bump or movements from your part simply mean that you have to start it all over again.

You will find three points like – A, B and C. A is an extreme point, B is the middle point and the C is another extreme point. You start the stopwatch and count the swings. When the bat starts from A and comes back to the same point (A) then only count 1.

After counting 10 swings, you can press the stop button on your stopwatch. You need to remember that the closer you can stop the watch, the more exact the result would be. You need to repeat this process at least 2 more times so that you can come to an average.

Now that you’ve repeated the same process altogether 3 times. Now count the total number of swings and the total number of duration as well. Now divide the total duration by the number of swings and what you get is the pendulum period of the bat. The common size and weight bats should have the pendulum period of 1.2 to 1.8.


Measuring the balancing point of the bat

We are going to measure the balancing point of the bat with the fingers. In this step, we have to measure the point where the bat balances horizontally and we must take the distance between that spot and the knob of the bat. The figure you find is called the balance point of the baseball bat. Try and get as accurate number as possible.


Exact weight of the bat

Now is the time to weigh the bat. You can say that it is already stated on the bat but, my suggestion is to make it on your own because most of the manufacturers do not state the exact weight of the bat on its body.

More so, when you add on handle grip and other external accessories, it certainly weighs more than the state figure. For better and exact measurement, you can use a kitchen scale or a digital scale where you can measure it on ounce scale. You need to realize the exact weight of the bat since this will help to get the most accurate MoI.


Time for some mathematics

Now that you have got the three very important variable measurements which are:

Pendulum period (T)

Balance point (d)

Bat weight (m)

Now we have a very simple equation to determine the Moment of Inertia (I) of the baseball bat. All we need to do is put these variable figures into the equation and calculate the result. What we get is the MoI. What is the equation then?

I = T2mgd/4π2

When we know everything, it should be quite easy for us to calculate the “I” from the given equation where “g” and “π” are constants. You just need to put the figures and use the calculator.


 As we have already found early in the discussion that greater inertia will make it more difficult to swing the bat, you can make this simple math while buying a baseball bat.

It may appear to be little complicated but when you do this for quite some time, you will get it easily then. There are some online moment calculators available to make the job easy, however, you need to get the variable measures right to have more accurate result.

Ricky J Oslen

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